Parity decomposition of a lag-two ARCH process
= Parity decomposition of a lag-two ARCH process
The stationary squared process has the positive series $X_t^2=\alpha_0\sum_{k\geq0}\alpha_2^k\prod_{j=0}^k\varepsilon_{t-2j}^2$. Even and odd observations therefore use disjoint families of <independent random variables>. This explains zero lag-one <covariance> of the squares despite dependence at lag two.